Volume 13, Issue 1
Several Variants of the Primal-Dual Hybrid Gradient Algorithm with Applications

Jianchao Bai ,  Jicheng Li and Zhie Wu

10.4208/nmtma.OA-2019-0030

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 176-199.

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  • Abstract

By reviewing the primal-dual hybrid gradient algorithm (PDHG) proposed by He, You and Yuan (SIAM J. Image Sci., 7(4) (2014), pp. 2526--2537), in this paper we introduce four improved schemes for solving a class of saddle-point problems. Convergence properties of the proposed algorithms are ensured based on weak assumptions, where none of the objective functions are assumed to be strongly convex but  the step-sizes in the primal-dual updates are more flexible than the previous. By making use of   variational analysis,  the global convergence and sublinear convergence rate in the ergodic/nonergodic sense are established, and the  numerical efficiency of our algorithms is verified by testing an image deblurring problem compared with several existing algorithms.

  • History

Published online: 2019-12

  • AMS Subject Headings

65K10, 65Y20, 90C90

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